Chapter 1 Testing the Significance of the Departures from Weak Separability

Admissible Clustering of Aggregator Components: A Necessary and Sufficient Stochastic Seminonparametric Test for Weak Separability

“…4 See Appendix 1 for computational details. 5 On extreme values, see Embrecht, Klüppelberg and Mikosch (2003) and Guégan (2003). 6 Note that such residuals are known as auxiliary residuals.…”

“…Following de Peretti (2005Peretti ( , 2007, de…ne the following binary relation: x i V Rx j if x i Rx j and x j P 0 x i or there if is exists a sequence between x i and x j such that x i Rx k and x k P 0 x i , x k Rx l and x l P 0 x k , ...,x m Rx j and x j P 0 x m . Also de…ne…”

“…Varian (1983), based on Varian (1982), has developed a procedure in order to test for weak separability that ignores the above condition (5). In order to meet the weak separability criterion, three conditions must be ful…lled, that is U (), f () and V () must exist.…”

“…For convenience, we will …rst assume that is known as well its distribution function. Since in (12) only few bundles are adjusted, the idea is to build a test tracking excess adjustments in some goods, and in particular to test whether or not extremes theoretical residuals are consistent with the perturbations induced by measurement error 5 . Statistically, we proceed as follows.…”

Testing for Weak Separability Using Stochastic Semi-Nonparametric Tests: An Empirical Study on Us Data

“…Thus, results based on this approach are often inconclusive. The test is extended in several directions by Swofford and Whitney (1994), Whitney (2003, 2005), Elger and Jones (2008), Cherchye et al (2015), and Barnett and de Peretti (2009), based upon de Peretti (2007). Varian (1985Varian ( , 1990 and Hjertstrand and Swofford (2014) can be referenced for extensions of GARP in stochastic environments.…”